Using data from
http://gensou-suwako.com/correct/URViewer/URrank.php I put together a tier list using the same methods that Smogon would use in their initial process to set up a tier list. After finishing that I decided to make some charts to look at how the metagame shapes up.
https://docs.google.com/spreadsheets/d/1fOra416UsiWZ1GX2u65IB-5B0gnQgIynf2wBY-7inRQ/edit#gid=1550230088&vpid=A1So of the 236 puppets available (Normal forms excluded) 54(~23%) are OU, 74(~31%) are UU, and 108(~46%) are NU.
Additionally of the 118 different characters 49 appear in OU which is about 41.5%.
Predictably lower costs tend to be lower tiered but not as much as you might expect.
As for coverage in OU, Earth and Electric hold the top while Wind is surprisingly lack luster being used mostly as Stab.
As for the OP types in the game. Appears as though Water and Wind are the strongest types with Electric shining through likely because of the prevalence of the other two.